Introduction Notation and Budget NDC systems Results Conclusions Appendix Increasing Life Expectancy and Pay-As-You-Go Pension Systems Markus Knell Oesterreichische Nationalbank Ninth Meeting of the Working Group on Macroeconomic Aspects of Intergenerational Transfers, Barcelona, 3 June 2013 *The content of these slides reflects the views of the authors and not necessarily those of the OeNB.
Introduction Notation and Budget NDC systems Results Conclusions Appendix Motivation • Pension systems have to cope with two two demographic developments: • Increases in life expectancy. • Fluctuations (and mostly declines) in fertility • I deal with the first aspect, since it represents an ongoing process with considerable and far-reaching budgetary consequences.
Introduction Notation and Budget NDC systems Results Conclusions Appendix Automatic Adjustment Rules • “Around half of OECD countries have elements in their mandatory retirement-income provision that provide an automatic link between pensions and a change in life expectancy [ . . . ] The rapid spread of such life-expectancy adjustments has a strong claim to be the most important innovation of pension policy in recent years” (OECD, Pensions at a Glance , 2011, p. 82). • Despite this claim there does not exist much research on this “most important innovation”.
Introduction Notation and Budget NDC systems Results Conclusions Appendix NDC systems I focus on the notional defined contribution (NDC) systems. Their basic features are:
Introduction Notation and Budget NDC systems Results Conclusions Appendix NDC systems I focus on the notional defined contribution (NDC) systems. Their basic features are: • Fixed contribution rate: τ ( t ) = � τ • Life-time assessment period • Past contributions are revalued with an appropriate notional interest rate • At retirement the notional capital is transformed into annual pension payments by taking the development of life expectancy into account • Advantages: Close relation between contributions and benefits; flexibility in retirement age with automatic reaction of the pension level to the age of retirement; individual accounts and annual statements increase transparency Orange envelope ); transnational portability. (
Introduction Notation and Budget NDC systems Results Conclusions Appendix Why focus on NDC? • It is increasingly popular (Sweden and around 10 other countries). • The World Bank, OECD and European Commission often use it as a reference points or benchmark to discuss reforms. • They are explicitely designed to deal with increasing life expectancy. • Other systems (German earnings-point, Austrian “notional defined benefit” system APG) can be directly related to it.
Introduction Notation and Budget NDC systems Results Conclusions Appendix Two crucial parameters
Introduction Notation and Budget NDC systems Results Conclusions Appendix Two crucial parameters • Notional interest rate (how past contributions to the pension system are revalued). • Remaining life expectancy (used to calculate the pension benefit at retirement).
Introduction Notation and Budget NDC systems Results Conclusions Appendix Two crucial parameters • Notional interest rate (how past contributions to the pension system are revalued). • Remaining life expectancy (used to calculate the pension benefit at retirement). Conventional wisdom: • Use the growth rate of the wage bill as the notional interest rate: “Viewed from a macroeconomic perspective, the ‘natural’ rate of return for an NDC system is the implicit return of a PAYG system: that is, the growth rate of the contribution bill” (B¨ orsch-Supan, 2003) • Use the cohort (i.e. forecasted) life expectancy: “The generic NDC annuity embodies [ . . . ] cohort life expectancy at the time the annuity is claimed” (Palmer, 2006).
Introduction Notation and Budget NDC systems Results Conclusions Appendix Main Finding
Introduction Notation and Budget NDC systems Results Conclusions Appendix Main Finding Both components of the conventional wisdom have to be modified: • It is sufficient to use periodic life expectancy to calculate the pension benefit. • One should use an “adjusted growth rate of the wage bill” as the notional interest rate.
Introduction Notation and Budget NDC systems Results Conclusions Appendix Notation 1 The generation born in period t has: • cohort size N ( t ) = N • life expectancy T ( t ) • retirement age R ( t )
Introduction Notation and Budget NDC systems Results Conclusions Appendix Notation 1 The generation born in period t has: • cohort size N ( t ) = N • life expectancy T ( t ) • retirement age R ( t ) NOTE 1: I assume that all members of one generation reach the cohort-specific maximum age T ( t ). NOTE 2: The maximum age observed in period t is denoted by T ( t ) and the retirement age by � � R ( t ). In general: T ( t ) � = � T ( t ) and R ( t ) � = � R ( t ).
Introduction Notation and Budget NDC systems Results Conclusions Appendix Notation 2 For generation t the PAYG system stipulates the following income streams: • Contributions: τ ( t + a ) W ( t + a ) for 0 ≤ a < R ( t ) • Pensions: P ( t , a ) for R ( t ) ≤ a ≤ T ( t ) NOTE: In NDC systems the contribution rate is fixed, i.e. τ ( t ) = ˆ τ .
Introduction Notation and Budget NDC systems Results Conclusions Appendix Budget of the PAYG system For the system in period t : • Labor force: L ( t ) = � R ( t ) × N � � T ( t ) − � � • Retired population: B ( t ) = R ( t ) × N � � T ( t ) R ( t ) P ( t − a , a ) d a � • Average pension: P ( t ) = T ( t ) − � � R ( t ) T ( t ) − � � • Dependency ratio: z ( t ) = B ( t ) R ( t ) L ( t ) = � R ( t ) • The balanced budget condition is given by: τ ( t ) W ( t ) L ( t ) = P ( t ) B ( t ) � �� � � �� � Revenue= I ( t ) Expenditure= O ( t ) Demographic steady-state
Introduction Notation and Budget NDC systems Results Conclusions Appendix The development of life expectancy An old controvery—How to best model life expectancy? Graph : • Life expectancy increases in a linear fashion T ( t ) = T (0) + γ · t • Robust relationsship: In the data: γ between 0 . 15 and 0 . 33. • From T ( t − � T ( t )) = � T ( t ) it follows that: � 1 T ( t ) = 1+ γ T ( t ).
Introduction Notation and Budget NDC systems Results Conclusions Appendix A formal expression of NDC Systems 1 • The notional capital before retirement: � R ( t ) � t + R ( t ) ρ ( s ) d s d a , K ( t , R ( t )) = τ W ( t + a ) e � t + a 0 where ρ ( s ) stands for the notional interest rate in period s . • The first pension payment: P ( t , R ( t )) = K ( t , R ( t )) Γ( t , R ( t )) , where Γ( t , R ( t )) is the remaining life expectancy of generation t at age R ( t ). • Existing pensions are adjusted according to: � t + a t + R ( t ) ϑ ( s ) d s , P ( t , a ) = P ( t , R ( t )) e where ϑ ( s ) stands for the adjustment rate in period s .
Introduction Notation and Budget NDC systems Results Conclusions Appendix A formal expression of NDC Systems 2 � � � R ( t − a ) � t − a + R ( t − a ) ρ ( s ) d s � � W ( t − a + b ) e d b t − a + b T ( t ) 0 � t t − a + R ( t − a ) ϑ ( s ) d s d a O ( t ) = � τ N e Γ( t − a , R ( t − a )) � R ( t )
Introduction Notation and Budget NDC systems Results Conclusions Appendix A formal expression of NDC Systems 2 � � � R ( t − a ) � t − a + R ( t − a ) ρ ( s ) d s � � W ( t − a + b ) e d b t − a + b T ( t ) 0 � t t − a + R ( t − a ) ϑ ( s ) d s d a O ( t ) = � τ N e Γ( t − a , R ( t − a )) � R ( t ) • Crucial task for the policymaker: Determine the control variables ρ ( t ), ϑ ( t ) and Γ( t , R ( t )) in such a way that expenditures develop in line with revenues I ( t ) = � τ L ( t ) W ( t ). • Question: Is this possible for any path of the retirement age R ( t ) (which is the choice variable of the households)?
Introduction Notation and Budget NDC systems Results Conclusions Appendix The first important parameter in NDC systems — The notional interest rate ˙ W ( t ) • Growth rate of average wages: ρ ( t ) = g W ( t ) = W ( t ) • Growth rate of the wage bill: ˙ ˙ W ( t ) L ( t ) ρ ( t ) = g W ( t ) + g L ( t ) = W ( t ) + L ( t )
Introduction Notation and Budget NDC systems Results Conclusions Appendix The first important parameter in NDC systems — The notional interest rate ˙ W ( t ) • Growth rate of average wages: ρ ( t ) = g W ( t ) = W ( t ) • Growth rate of the wage bill: ˙ ˙ W ( t ) L ( t ) ρ ( t ) = g W ( t ) + g L ( t ) = W ( t ) + L ( t ) Conventional wisdom: Use the growth rate of the wage bill.
Introduction Notation and Budget NDC systems Results Conclusions Appendix An important caveat • If the retirement age increases, then the labor force grows – even if the cohort size is constant. ˙ � L ( t ) = � R ( t ) R ( t ) N → g L ( t ) = � R ( t ) • Increases in the retirement age are, however, necessary to stabilize the dependency ratio z ( t ). In particular: T ( t ) − � � R ( t ) z ( t ) = = � z implies that: � R ( t ) � T ( t ) T ( t ) � R ( t ) = z = 1 + � (1 + γ )(1 + � z ) γ • In this case: g L ( t ) = T ( t )
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